scholarly journals Length spectra andp-spectra of compact flat manifolds

2003 ◽  
Vol 13 (4) ◽  
pp. 631-657 ◽  
Author(s):  
R. J. Miatello ◽  
J. P. Rossetti
Keyword(s):  
Compact Flat Manifolds ◽  
Flat Manifolds

Isospectral compact flat manifolds

1992 ◽  
Vol 68 (3) ◽  
pp. 489-498 ◽  
Author(s):  
Isabel Dotti Miatello ◽  
Roberto J. Miatello
Keyword(s):  
Compact Flat Manifolds ◽  
Flat Manifolds

scholarly journals Representation Equivalent Bieberbach Groups and Strongly Isospectral Flat Manifolds

2014 ◽  
Vol 57 (2) ◽  
pp. 357-363
Author(s):  
Emilio A. Lauret
Keyword(s):  
Isometry Group ◽  
Regular Representations ◽  
Compact Flat Manifolds ◽  
The Right ◽  
Flat Manifolds ◽  
Full Isometry Group

AbstractLet Γ1 and Γ2 be Bieberbach groups contained in the full isometry group G of ℝn. We prove that if the compact flat manifolds Γ1\ℝn and Γ2\ℝn are strongly isospectral, then the Bieberbach groups Γ1 and Γ2 are representation equivalent; that is, the right regular representations L2(Γ1\G) and L2(Γ2\G) are unitarily equivalent.

scholarly journals FINITE FLAT SPACES

Mathematika ◽  
2019 ◽  
Vol 65 (4) ◽  
pp. 1010-1017
Author(s):  
Vladimir Zolotov
Keyword(s):  
Lie Groups ◽  
Metric Spaces ◽  
List Type ◽  
Euclidean Spaces ◽  
Markov Type ◽  
Finite Metric Space ◽  
Isometric Actions ◽  
Compact Flat Manifolds ◽  
Flat Manifolds

We say that a finite metric space $X$ can be embedded almost isometrically into a class of metric spaces $C$ if for every $\unicode[STIX]{x1D716}>0$ there exists an embedding of $X$ into one of the elements of $C$ with the bi-Lipschitz distortion less than $1+\unicode[STIX]{x1D716}$. We show that almost isometric embeddability conditions are equal for the following classes of spaces.(a)Quotients of Euclidean spaces by isometric actions of finite groups.(b)$L_{2}$-Wasserstein spaces over Euclidean spaces.(c)Compact flat manifolds.(d)Compact flat orbifolds.(e)Quotients of connected compact bi-invariant Lie groups by isometric actions of compact Lie groups. (This one is the most surprising.)We call spaces which satisfy these conditions finite flat spaces. Since Markov-type constants depend only on finite subsets, we can conclude that connected compact bi-invariant Lie groups and their quotients have Markov type 2 with constant 1.

Spectral Properties of Four-Dimensional Compact Flat Manifolds

2006 ◽  
Vol 29 (1) ◽  
pp. 17-50 ◽  
Author(s):  
Roberto J. Miatello ◽  
Ricardo A. Podestá
Keyword(s):  
Spectral Properties ◽  
Compact Flat Manifolds ◽  
Flat Manifolds

scholarly journals Profinite genus of the fundamental groups of compact flat manifolds with holonomy group of prime order

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Genildo de Jesus Nery
Keyword(s):  
Fundamental Group ◽  
Prime Order ◽  
Isomorphism Class ◽  
Holonomy Group ◽  
Fundamental Groups ◽  
Flat Manifold ◽  
Profinite Completion ◽  
Compact Flat Manifolds ◽  
Flat Manifolds

Abstract In this article, we calculate the profinite genus of the fundamental group of an 𝑛-dimensional compact flat manifold 𝑋 with holonomy group of prime order. As consequence, we prove that if n ⩽ 21 n\leqslant 21 , then 𝑋 is determined among all 𝑛-dimensional compact flat manifolds by the profinite completion of its fundamental group. Furthermore, we characterize the isomorphism class of the profinite completion of the fundamental group of 𝑋 in terms of the representation genus of its holonomy group.

Sign in / Sign up

Export Citation Format

Share Document